1. RIZZO CARMELO Isospin effects in heavy ion reactions at low energies
Laboratori Nazionali del Sud (Catania)
Università degli studi di Catania
M.Colonna, M.Di Toro(LNS,Catania)
V.Baran (NIPNE HH,Bucharest)
4th International Symposium on the Nuclear Symmetry Energy NuSYM14 University of Liverpool, UK July 7-9, 2014

2. VLASOV + NN-COLLISIONS and PAULI CORRELATIONS :
In medium cross sections +
Fluctuations (SMFapproach)
gain
loss
Chomaz,Colonna, Randrup
Phys. Rep. 389 (2004)
Stochastic extension of microscopic transport equation BNV, following a test-particle time evolution
SELF-CONSISTENT MEAN FIELD: Skyrme standard parameterization
SOFT: A = -358,1MeV; B = 304,8MeV; σ = 7/6 → K=201MeV
STIFF: A = -123,6MeV; B = 70,4MeV; σ = 2 → K=377MeV
Asy-STIFF
SYMMETRY ENERGY:
Asy-SOFT
Neutron Stars
- mass/radius
-”hybrid structure”
Neutron Skin
Pigmy Resonances
Phys.Rep. 410 (2005)

3. Heavy Ion Collisions (HIC) allow one to explore the behavior of nuclear matter under several conditions of density, temperature,
spin, isospin, …
HIC from low to Fermi energies (~10-60 MeV/A) are a way to probe the density domain just around and below normal density.
The reaction dynamics is largely affected by surface effects, at the
borderline with nuclear structure.
Varying the N/Z of the colliding nuclei (up to exotic systems) , it becomes possible to test the isovector part of the nuclear interaction
(symmetry energy) around and below normal density.

4. 197Au + 197Au collisions were studied at 15AMeV energy (LNS)
197Au + 197Au collisions were studied at 15AMeV energy (LNS). An interesting process of violent reseparation of this heavy system into three or four fragments of comparable size was observed. PHYSICAL REVIEW C 81, (2010)
Y.Li et al., ImQMD calculations. NPA (2013) F1 F2 F3
In-plane velocity distribution of fragments. Points represent velocities of fragments F1, F2, and TLF in each event, plotted in the laboratory reference frame as a function of the longitudinal and transversal components.
Mass spectrum of PLF’s obtained by the event-by-event addition of mass numbers of fragments F1 and F2, compared with (a) the mass spectrum of TLF’s.

5. 197Au + 197Au collisions: shape analysis of SMF events
Semiperipheral heavy ion collisions in the beam energy range of MeV/nucleon: the reaction mechanism is heavily dominated by the occurrence of fragment quadrupole and octupole deformations in the exit channel.
The possibility of observing ternary breakup processes of dynamical origin is explored within the SMF model, looking at the concurrent role of surface mean-field instabilities, dissipative anf angular momentum effects.
The procedure based on the study of shape deformations, which was introduced in PHYSICAL REVIEW C 813, (2011)
to evaluate fusion vs. breakup cross sections, is extended here to the search of multiple breakup processes
Q2 = ∫ρ(r)(3z2 − r2)dr
Q3 = ∫ ρ(r)z(5z2 − 3r2)dr
Alignment:
The smallest fragment
acquire the largest velocity
We assume that, after the DF has reached its maximum degree of deformation, it will split in two pieces.
The neutron-rich neck region connecting the two reaction partners survives quite a long time favouring the development of surface instabilities and mean-field fluctuations, leading to a variety of configurations for the reaction outcome.

6. 197Au + 197Au collisions: shape analysis of SMF events
Neck rupture coupled to angular momentum effects, which could explain the experimental observation.
The PLF-TLF distribution in the plane for the reaction at 23 MeV/A
A2half, integrating density from the left extreme up to the center. The masses of the largest (A2) and smallest (A1) fragments which may originate from the break-up of the DF fragments are evaluated as:
A2 = 2 A2half and A1 = ADF − A2
The mass distribution of
DF____ and SF _ _ _ fragments
The DF fragment is systematically larger
The masses are normalized to the average mass of the DF fragments, results look in good agreement with experimental data.

7. Pre-equilibrium neutron-rich emission and/or evaporation.
The distribution corresponding to the geometrical weigth of the two impact parameters
The average N/Z ≈ 1.43 ratio of the whole system, is lower than the initial asymmetry, N/Z = 1.49
Pre-equilibrium neutron-rich emission and/or evaporation.
The lightest fragments are slightly proton-richer:
Coulomb polarization effects, because light fragments are located at the outer side of the system.
F1 the fragment located on the external side of the DF fragment and as F2 the other one.
The statistical fission processes of PLF/TLF fragments is neglected in our analysis

8. Quadrupole moment of primary fragments
Fragment Deformations : 132Sn + 64Ni Elab = 10 MeV/A . SPES – SPIRAL2
132Sn + 64Ni , E/A = 10 MeV, b = 7 fm
3 events, t = 500 fm/c
Binary events at freeze-out time ≈ 500fm/c. Each EOS: 200 events/b
Quadrupole moment of primary fragments
b=6fm b=7fm b=8fm
Asystiff case:
larger residue deformations
→ more dissipative neck dynamics!
→ more break-up
→ more ternary/quaternary events
Asysoft
Asystiff
The symmetry repulsion at low densities in the linear (stiff) choice:
the neutron-rich neck connecting the two partners can survive a longer time producing very deformed final fragments, eventually leading to ternary/quaternary fragmentation events.
M.Colonna et al., Spiral2 LOI Oct.2006

9. Isospin migration in neck fragmentation
Transfer of asymmetry from PLF and TLF to
the low density neck region: neutron enrichment
of the neck region
Effect related to the derivative of the symmetry
energy with respect to density
Asymmetry flux
ρIMF < ρPLF(TLF)
Sn112
+ Sn112
Sn124
+ Sn124
b = 6 fm, 50 AMeV
stiff - full
Density gradients derivative of Esym
J.Rizzo et al.
NPA806 (2008) 79
PLF, TLF
neck
emitted
nucleons
asy-soft
asy-stiff
Larger derivative with asy-stiff
larger isospin migration effects
The asymmetry of the neck is larger than
the asymmetry of PLF (TLF) in the stiff case

10. Comparison with Chimera data
Properties of ‘dynamically emitted’ (DE) fragments
Charge distribution
Parallel velocity distribution
Good reproduction of overall dynamics
The N/Z content of IMF’s in better reproduced
by asystiff (L =75 MeV) DE
124Sn + 64Ni 35 AMeV SE
E. De Filippo et al., PRC(2012)
see also Brown et al, PRC87,061601(2013)

11. Charge equilibration

12. Charge equilibration in fusion and D.I. collisions
D(t) : bremss. dipole radiation CN: stat. GDR
Initial Dipole A1 A2
TDHF
calculations
If N1/Z1 ≠ N2/Z2
Relative motion of neutron and proton centers of mass
Simenel et al,
PRC 76, (2007)
SMF simulations
132Sn + 58Ni , D0 = 45 fm
E/A = 10 MeV
40Ca + 100Mo
E/A = 4 MeV
stiff
soft
C.Rizzo et al., PRC 83,
(2011)
V.E.Oberacker et al., PRC 85,
(2012)

13. Dynamical dipole (DD) emission: a ‘robust’ collective mechanism
Bremsstrahlung:
Quantitative estimation
V.Baran, D.M.Brink, M.Colonna, M.Di Toro, PRL.87 (2001)
H.L.Wu et al. , Isospin dependent (ID) QMD model
40Ca + 48Ca, Ebeam = 10 MeV/A, b = 4 fm
10 MeV/A
The dipole mechanism is clearly observed also
In Molecular Dynamics calculations
M. Papa et al., CoMD model
LNS experiment - binary collisions

14. Dynamical dipole (DD) emission and symmetry energy
B.Martin et al., PLB 664 (2008) 47
36Ar + 96Zr
40Ar + 92Zr
Bremsstrahlung:
Quantitative estimation
V.Baran, D.M.Brink, M.Colonna, M.Di Toro, PRL.87 (2001)
soft
Experimental evidence of the extra-yield (LNL & LNS data)
stiff
D(0) ~ 18 fm
16O + 116Sn
D(0) = 8.6 fm
in-medium n-n cross sections
soft
MEDEA
@ LNS
A.Giaz et al, submitted to PLB
stiff
A.Corsi et al., PLB 679, 197 (2009), LNL experiments
D.Pierroutsakou et al., PRC80, (2009)

15. Dynamical dipole (DD) emission: sensitivity to n-n cross-section (c-s)
D.Pierroutsakou et al., PRC80, (2009)
reduced c-s
in-medium c-s
free c-s
1) Important to check and fix the n-n cross section pre-equilibrium particle emission
2) Enhance the sensitivity to symmetry potential (S0,L) reactions with large D(0)
V. Baran et al., PRC79, (R) (2009)
asy-soft
larger symmetry energy,
Bigger DD (30 % larger than asy-stiff !)
vs for Mγ
Sensitivity to EOS may become
larger than exp. error bars
132Sn + 58Ni , D0 = 45 fm
124Sn + 58Ni, D0 = 33 fm
soft
stiff

16. Dynamical dipole emission in very n-rich systems
See LoI’s by
Pierroutsakou and Casini
132Sn + 58Ni , D0 = 45 fm
124Sn + 58Ni, D0 = 33 fm
Asysoft
larger symmetry energy,
Bigger DD (30 % larger than Asystiff !)
soft
vs for Mγ
stiff
Sensitivity to EOS may become
larger than exp. error bars
V. Baran et al., PRC79, (R) (2009)

17. → Low energy: time scales for break-up not compatible with transport equation treatment.
Is it possible to extract the fusion probability from the early dynamics of the system ?
σ( l )n-rich - sensitivity to the asy-EOS?
We make an attempt to describe by a new method, the fusion spin distribution in the framework of a semi-classical transport theory with a phase space shape analysis.
Time evolution of Quadrupole
moment in coordinate space: z
Q(t) =< 2z2(t) − x2(t) − y2(t) > z z
and in momentum space in a
region around the center of mass:
QK(t) =< 2pz2(t) − px2(t) − py2(t) >
Interesting perspectives are opening for new experiments on low energy collisions with exotic beams focused to the study of the symmetry term below and above saturation density.
We consider the reactions 132Sn + 64,58Ni at low energy, 10AMeV, to study isospin and symmetry energy effects on the competition between reaction mechanisms: fusion vs break-up (deep-inelastic).

18. THE PROMPT DIPOLE MODE
In the fusion or deep-inelastic channels, the Dipole mode is present almost with the same strength in b=5.5fm and 6fm.
In the Asysoft we have a systematic increase of the yields of about 40% more than in the Asystiff case:
The results are a good indication that the prompt dipole oscillation is taking place in a deformed system, where low density surface contributions are important(larger restoring force corresponding to mean densities below saturation for asySoft).
D(t) = NZ/A X(t)
”bremsstrahlung”
The onset of the dipole mode is delayed with respect to the first high density stage of the neck region since the composite system needs some time to develop a collective response of the mean field.
In this way fusion and dynamical dipole data can be directly used to probe the isovector part of the in-medium effective interaction below and above ρ0

19. Summary Collaborators: V.Baran (NIPNE HH,Bucharest)
Competition between reaction mechanisms at lower energy
Process of separation of heavy system into three or four fragments are simulated to investigate the main modes of re-separation of a heavy nuclear system.
BNV Analysis to extract the experimental mass distribution of Au+Au at 15-23AMeV
Study of the reaction mechanisms at 23AMeV: strong neck instability.
A larger gamma-ray emission from the more charge asymmetric channel was evidenced, in the Giant Dipole Resonance energy range
Isospin effects are revealed just selecting into “exotic”experiments the impact parameter window corresponding to semi- peripheral reactions. We suggest some observables:
Fusion vs. Break-up probabilities in the centrality transition region;
Fragment deformations in break-up processes and probability of ternary/quaternary events;
γ-multiplicity and anisotropy of the Prompt Dipole Radiation, for dissipative collisions in charge asymmetric entrance channels.
Collaborators: V.Baran (NIPNE HH,Bucharest)
M.Di Toro, M. Colonna (LNS, Catania)

20. 197Au + 197Au collisions are evaluated by BNV simulations at 15AMeV energy.
F2=2 x N1part
F1= Ntot – F2
N1part
Density cut at 0,04fm-3
Density cut at 0,04fm-3

21. Competition between reaction mechanisms: fusion vs deep-inelastic
36Ar + 96Zr ,
E/A = 9 MeV
Fusion or
break-up ?
Important role of fluctuations
Fusion probabilities may depend on the N/Z of the reaction partners:
- A mechanism to test the isovector part of the nuclear interaction
C.Rizzo et al., PRC83, (2011)

22. reverse trend in the 132Sn+58Ni system in the most peripheral b.
Competition between reaction mechanisms: fusion vs deep-inelastic at low energy.
Time evolution of the Quadrupole moment in coordinate space along symmetry axis (degree of deformation of the dynuclear system) for the two choices of the symmetry term. PHYSICAL REVIEW C 813, (2011)
Look at values of the slope to perform an analysis of the deformation velocity of the dinuclear system that is going to a break-up exit channel.
(slightly) larger sistematic deformation in the asy-styff case in the 132Sn+64Ni system;
reverse trend in the 132Sn+58Ni system in the most peripheral b.
Transition from fusion to a break-up mechanism
The break-up probability enhanced if the slope of quadrupole moment in r space is more positive.

23. The fusion probabilities are isospin dependent;
Competition between reaction mechanisms: fusion vs deep-inelastic at low energy.
Just from this simple analysis of the quadrupole we can already see that:
The fusion probabilities are isospin dependent;
The asysoft choice seems to lead to larger fusion cross sections between b=5.0 and 6.5 fm.
These results will be nicely confirmed introducing a more quantitative approach based on the correlation to the quadrupole deformation in momentum space.

24. Competition between reaction mechanisms: fusion vs deep-inelastic at low energy.
Time evolution of the Quadrupole moment evaluated in momentum space along symmetry axis, into a sphere of radius 3fm and center in the center of mass, in reactions of transfer angular momentum
Increasing impact parameter the quadrupole QK(t) becomes more negative in the time interval from 150 to 300 fm/c:
the perpendicular components to the symmetry axis are increasing.
We can interpret it as due to the presence of a region where Coriolis forces are enhanced when the angular momentum is larger. These forces can break the deformed dinuclear system.
The break-up probability enhanced if the quadrupole moment in p space is more negative.

25. Asy Stiff Asy Stiff Asy Soft Asy Soft
How to extract the fusion probability from early evolution of the system?
Combine the information from the two observables (Q’ and QK ) and select positive Q’ and negative QK for break-up.
Break-up
Break-up
Asy Stiff
Asy Stiff
Asy Soft
Asy Soft
For each impact parameter Nfusion=Ntot–Nbreak-up → Pbreak-up= A1Gauss•A2Gauss A1<0 and A2>0

26. Angular momentum distributions of the fusion cross sections:
The absolute value of the σfusion presents a good agreement with recent data for 132Sn+64Ni, at lower energy ( ∼5AMeV), taken at the ORNL;
J.F. Liang et al., Phys. Rev. C75, (2007)
the difference in area is about 4-5 % for the neutron rich system ;
in the transition centrality region there is a difference between the σfusion corresponding to the different EOS, with larger values for Asy-soft.
P. FROBRICH PLB(1990)
The results are comparated with the macroscopic code Pace4.
Through a selection in angular momentum, 130<l<180, we find that the asysoft curve is above the asystiff (10-15%).
It can be then compared to experimental data as evidence of sensitivity to the density dependence of the symmetry energy!
1128mb/ 1078mb
1020mb/ 1009mb
σfusion show a larger diffuseness in the neutron rich system.

27. ANALYSIS OF THE SYMMETRY ENERGY EFFECTS d(t)Rproj/(Rproj+Rtarghet)
The larger fusion probability with the asysoft choice indicate that the reaction mechanism is regulated by a symmetry term at suprasaturation density, where the Asysoft EOS is less repulsive for the neutrons.
Asysoft choice has a systematic larger isospin, consistently with the presence of a less repulsive neutron potential at densities just above saturation.
This is confirmed by the separate behavior of the numbers of neutron and proton.
The densities found in the asysoft case are above the asystiff, to confirm the expectation of a smaller equilibrium density for a stiffer symmetry term;
the monopole oscillations are present, showing that also at these low energies we can have some compression energy.
Initial average isospin asymmetry
The N/Z oscillations after 100fm/c can be related to the excitation of isovector density modes in the composite system during the path to fusion or break-up.